Coding for a Single Sparse Inverse Problem

We propose a coded computing technique for making the power-iteration method of solving a single sparse linear inverse problem robust to erasure-type noise. We observe that for sparse inverse problems, codes with dense generator matrices can significantly increase storage costs. Thus, we propose coding the power-iteration computation using sparse generator matrices. Surprisingly, despite the poor error-correction ability of codes with sparse generator matrices, we show through both theoretical analysis and simulations that these codes are sufficient to achieve almost the same convergence rate as noiseless power iterations, provided that a new decoding algorithm that we call “substitute decoding” is used.